Problem: Suppose that $2x^2 - 5x + k = 0$ is a quadratic equation with one solution for $x$. Express $k$ as a common fraction.
If the quadratic equation has exactly one solution, then the discriminant, $5^2 - 4 \cdot 2 \cdot k = 25 - 8k$, must be equal to zero. Thus, $25 - 8k = 0 \Longrightarrow k = \boxed{\frac{25}{8}}$.